Exchange rate pass-through to various price indices: empirical estimation using vector error correction models

Faculty of Business, Economics and Social Sciences

Department of Economics

Exchange rate pass-through to various price

indices: empirical estimation using vector error

correction models

DISCUSSION PAPERS

Exchange rate pass-through to various price indices:

empirical estimation using vector error correction

models

Andreas Bachmann

May 24, 2012

Abstract

The extent to which exchange rate fluctuations are passed through to domestic prices is of high relevance for open economies and for monetary authorities targeting price stability. Existing empirical studies estimating the exchange rate pass-through for Switzerland are based on either single equation estimation or on VAR models. How-ever, these approaches feature some major drawbacks. The former cannot account for dynamic interactions between the time series and both methods disregard long-run equilibrium relations between the variable levels. This paper contributes to the evidence on the exchange rate pass-through in Switzerland by using a vector error correction model, which has the advantage of incorporating both short-run dynamics and long-run equilibrium relations among variables. The results reveal a significant impact of exchange rate shocks on various price (sub-)indices. Pass-through to import prices is substantial both in the short-run and in the long-run and occurs relatively quickly. It is slower, but still considerable in the long-run for the consumer price index and some of its sub-indices. Producer prices react signif-icantly to exchange rate shocks as well. In contrast, consumer price inflation for services and for goods of domestic origin show hardly any significant response. The findings of this paper indicate a decline in the pass-through over time.

JEL classification: E31, F31, F41

Keywords: Exchange rate pass-through, consumer prices, import prices, cointegra-tion, vector error correction models, new open economy macroeconomic model

∗_{University of Bern, Department of Economics, Schanzeneckstrasse 1, P.O. Box 8573, CH-3001 Bern,}

Switzerland, email: [email protected]

I thank Prof. Dr. Klaus Neusser and Stefan Leist for helpful comments and the Swiss National Bank and the Swiss Federal Customs Administration for providing data.

1

Introduction

Exchange rates are of crucial importance for open economies. Due to their impact on the relative prices between domestic and foreign goods, exchange rates affect the demand for these goods. As a consequence, both aggregate production and price levels of an open economy depend on exchange rates. The influence of exchange rates on domestic prices has long been of interest in the international macroeconomics literature because it matters for the international transmission of shocks and international policy spillovers. The extent to which prices change in response to exchange rate fluctuations, henceforth referred to as exchange rate pass-through (ERPT), is of particular importance for monetary policy. Central banks aiming at stabilizing prices need to know about the inflationary effect of exchange rate movements. This knowledge is essential for both their inflation forecasts and the monetary transmission mechanism. In recent years, there has been extensive research, theoretical as well as empirical, on the determinants, the dynamics and the extent of the ERPT. The massive exchange rate fluctuations in the aftermath of the recent financial crisis and international debt crisis have reinforced the interest in the ERPT.

Theoretical papers have revealed a variety of factors influencing the ERPT, such as international price discrimination (Krugman, 1986), openness of an economy, degree of competition (Dornbusch, 1987), transportation and distribution costs (Burstein et al., 2003a,b, 2005; Corsetti and Dedola, 2005), the currency pricing decision (Bacchetta and van Wincoop, 2005) in combination with the degree of price stickiness, stability of mone-tary policy (Devereux and Engel, 2001; Devereux et al., 2004), the perceived persistence of exchange rate movements (Froot and Klemperer, 1989; Taylor, 2000), and exchange rate volatility (Corsetti and Pesenti, 2004). Thus, the ERPT to prices has been recognized as an important and complex transmission mechanism.

Given this variety of country-specific factors that affect the pass-through, empirical estimations for one country do not apply to other countries. Instead, separate estimations have to be conducted for different countries. Based on the methods applied, the empirical papers can be classified into three groups: studies based on single equation models, vector autoregressive (VAR) models and cointegration analysis (including vector error correction (VEC) models).

In single equation models, a price or inflation measure is regressed on the exchange rate and further explanatory variables (see Menon, 1995, for a survey of early contributions; more recent examples of studies applying this method are Gagnon and Ihrig, 2004, and Campa and Goldberg, 2005). The findings of these papers show substantial variation in the estimated degree of ERPT across countries.

Many studies based on VAR models (e.g. McCarthy, 2000; Hahn, 2003; Choudhri et al., 2005; Cavaliere, 2007) find evidence for significant ERPT to import prices and limited pass-through to producer and consumer prices. Moreover, the results indicate

that the magnitude of the ERPT and the speed of price adjustments decrease along the distribution chain.

Evidence on the ERPT based on the analysis of cointegrating relations or VEC models is rather scarce. Both Kim (1998) and Billmeier and Bonato (2004) find a relatively small long-run impact of exchange rates on price levels. In contrast, the findings of Masten (2004), who analyzes depreciation and inflation rates instead of exchange rates and price levels, suggest a high ERPT.

For Switzerland, evidence on the ERPT indicates a decreasing degree of pass-through along the distribution chain. Import prices react more quickly and to a larger extent to exchange rate shocks than consumer prices. The estimated degree of pass-through varies substantially between studies. The evidence for Switzerland is based on both single equation models (Gagnon and Ihrig, 2004; Campa and Goldberg, 2005) and VAR models (McCarthy, 2000; Cavaliere, 2007; Stulz, 2007).

However, the ERPT to Swiss prices has not yet been analyzed in the framework of a VEC model. Moreover, evidence on the ERPT using VEC models is in general scarce, despite the advantages of this estimation method. In particular, VEC models feature the advantage of incorporating both short-run dynamic interactions between the variables and long-run equilibrium relations contained in the variable levels. Since both the dynamics and the short- and long-run degree of ERPT are of interest, VEC models appear to be appropriate for estimating the ERPT.

Many studies on the ERPT have restricted their analysis to the impact of exchange rate shocks on aggregate price indices such as the import or consumer price index. However, a better understanding of the complex ERPT mechanism might be achieved by additionally estimating the pass-through to various price indices, such as consumer price sub-indices for imported goods, for domestically produced goods or for services. Up to now, little research has been devoted to the ERPT to price sub-indices.

This master thesis estimates the ERPT to various price (sub-)indices for Switzerland. The purpose of the paper is twofold. Firstly, it contributes to the existing evidence on the ERPT by using a more complex and more appropriate model for estimation, namely a VEC model. Based on the estimated VEC models, this master thesis analyzes the degree of pass-through (both in the short- and in the long-run) as well as the dynamics of the price adjustments over time. Secondly, by estimating the ERPT to prices for specific categories of goods, this paper aims to shed some more light on the complex transmission mechanism from exchange rates to prices. The estimated responses of price sub-indices to exchange rate shocks may promote the understanding of the determinants, the degree and the dynamics of the ERPT to the aggregate consumer price index.

The results of this master thesis reveal a significant impact of exchange rate shocks on aggregate import, producer and consumer price indices. In the short-run, the ERPT decreases along the distribution chain: The pass-through is much higher for import prices

than for producer and consumer prices. Moreover, the ERPT to import and producer prices occurs more quickly than the pass-through to overall consumer prices. The analy-sis of the price adjustment dynamics shows that, with some lag, the response of import prices to exchange rate shocks resembles the response of the exchange rates. In contrast, producer and consumer prices mostly converge steadily to their new long-run values. The comparison of the long-run price adjustment due to exchange rate shocks to the long-run change in exchange rates shows substantial pass-through to import, producer and consumer prices. However, the long-run pass-through estimates are very imprecise. Therefore, the findings for the long-run need to be interpreted with care. Nevertheless, some long-run ERPT estimates are significantly different from zero, indicating that ex-change rate shocks have a considerable long-run impact on import and consumer prices. Thus, the ERPT is important for any institution that forecasts inflation, in particular for central banks. Overall, the findings of this thesis are consistent with previous ERPT estimates for Switzerland.

In addition, the results of this paper show that pass-through varies considerably be-tween different consumer price sub-indices. Consumer price inflation both for services and for goods of domestic origin show hardly any significant response to exchange rate shocks, whereas the consumer price sub-indices for goods and for goods of foreign origin react significantly. An analysis of several subsamples indicates that the ERPT has declined over time for all price (sub-)indices. Robustness checks show that many results of the VEC models are rather similar to results obtained from a VAR model, but that the VAR model tends to find somewhat lower pass-through estimates to many price indices.

The remainder of this paper is structured as follows. Section 2 reviews theoretical and empirical literature on the ERPT. A theoretical model of the ERPT in a framework of international strategic price setting and the implications of the theoretical analysis are presented in section 3. Section 4 describes the methodology, the model and the identification strategy used for the empirical analysis. Section 5 contains the description of the data. In section 6, the estimation and the empirical results are presented. Some comparisons and robustness checks are discussed in section 7. Section 8 concludes.

2

Literature review

2.1

Theoretical literature

This section contains an overview of theoretical papers about the ERPT to prices. Sub-section 2.1.1 briefly introduces two basic economic relations between exchange rates and prices. The main focus of this section is on the importance of strategic price setting and imperfect competition for the ERPT (subsection 2.1.2). Other branches of the literature are briefly reviewed in subsection 2.1.3.

2.1.1 Purchasing power parity and the law of one price

A fundamental relation between exchange rates and prices is given by the purchasing power parity (PPP), which states that once converted to a common currency, national price levels should be equal. International arbitrage is the main justification why this relation should hold. The same relation on a more disaggregated level is called the law of one price. For each good j, the price in domestic currency (Pj) is equal to the foreign

price (P_j∗) converted to the domestic currency:

Pj =SPj∗. (1)

S denotes the nominal exchange rate, defined as the price of foreign currency in terms of domestic currency. The law of one price, which is motivated by international arbitrage, is an important requirement for PPP to hold.1

Even in this simple framework of PPP and the law of one price, the relation between prices and exchange rates may differ across countries. For a small country with no in-fluence on world market prices, the law of one price would imply unitary pass-through of exchange rates to prices (i.e. a depreciation of the domestic currency by one percent would lead to an increase of the domestic price by one percent). However, if the exchange rate of a large economy depreciates, the upward pressure on domestic prices is partly offset by a reduction in the world price resulting from lower world demand. This reduces the measured pass-through for large economies. Hence, the size of an economy is one determinant of the extent of the ERPT to prices (McCarthy (2000), p.3).

2.1.2 Pricing to market and imperfect competition

Models with deviations form the law of one price provide further insight into the ERPT to prices. The reasons for these deviations often reveal important determinants of the ERPT. One important factor is imperfect competition. With absence of international arbitrage, firms can price discriminate between different locations. A theoretical basis for the relation between exchange rates and prices in the context of international price discrimination is provided by Krugman (1986) and Dornbusch (1987).

Krugman (1986) discusses several static and dynamic models with respect topricing to market, a term henceforth extensively used in the literature. Pricing to market describes the (non-competitive) pricing behaviour of firms to strategically choose prices in different markets and to incompletely adjust prices to exchange rate movements, but to adjust profit margins instead. Comparing static models, Krugman finds that pricing to market

1_{However, the law of one price holding does not necessarily imply that PPP holds. One particular reason}

is the existence of non-tradable goods. Prices of non-tradable goods may differ across countries, causing a violation of PPP. According to the Balassa-Samuelson model, differences in the prices of non-tradable goods arise because of productivity differentials (Asea and Corden (1994)).

behaviour can arise in case of limited competition (Cournot oligopoly and monopolistic price discrimination), but not in a simple competitive framework. To get pricing to market behaviour, the competitive model needs to be enlarged by transportation or distribution costs.

In the discussion of some dynamic models, Krugman argues that if the adjustment of a firm’s service and distribution infrastructure is costly, the expected persistence of exchange rate changes plays an important role for the ERPT. A firm is not willing to bear the adjustment costs if the exchange rate change is expected to reverse soon. Using other models, Froot and Klemperer (1989) and Taylor (2000) obtain similar conclusions: The more persistent an exchange rate change is perceived to be, the larger is the price adjustment.

Moreover, Krugman (1986) argues that if the adjustment costs are increasing in the speed of adjustment, prices would only gradually be adjusted even in the case of a perma-nent exchange rate change. Hence, the time elapsed after the exchange rate change is of importance. Krugman concludes that dynamic models of imperfect competition might be the most suitable models to explain pricing to market. Such a model is used in section 3.1 to analyze the ERPT to prices.

The paper of Dornbusch (1987) is another seminal theoretical contribution that em-phasizes the role of imperfect competition for the ERPT. Similar to Krugman (1986), Dornbusch (1987) adopts a partial-equilibrium approach in the sense that movements in the exchange rate are assumed to be exogenous. The Cournot oligopoly model with a homogeneous good, a linear demand function and a number of domestic and foreign firms is able to explain the whole range of exchange rate induced price changes between the two limiting cases of unchanged prices on the one hand and complete ERPT (i.e. price adjustments proportional to the exchange rate change) on the other hand. Two factors determine the magnitude of the ERPT: the number of foreign firms relative to the total number of firms and the ratio of marginal costs of foreign firms to the price (the inverse of the mark-up). The former can be considered as a proxy for the share of imports; the latter is a measure of the degree of competition. According to this model, the ERPT is higher for countries with a large import share because, in this case, more firms face a change in their marginal costs when exchange rates change. Moreover, the ERPT increases with the degree of competition because this reduces the ability of firms to absorb exchange rate induced cost shocks by adjusting profit margins instead of changing prices.

Dornbusch (1987) discusses several additional models and concludes that all these models predict a reduction of import prices after an appreciation. Whether and to what extent the domestic firms adjust their prices depends on the specific model.

2.1.3 Review of theoretical considerations

The preceding subsection discussed the ERPT to prices in the context of imperfect compe-tition. This subsection gives a summary of alternative approaches to the ERPT. Following Engel (2004), there are two distinct branches of the literature modelling the phenomenon that import prices react less than proportionally to exchange rate movements. One con-sists of mostly partial equilibrium models with flexible prices and imperfect competition. The other part of the literature is general equilibrium in nature and emphasizes the role of nominal price stickiness. Thus, it is mainly focussing on the ERPT in the short-run. When prices are sticky, it is important whether the foreign firms set their prices in their own currency (producer currency pricing, PCP) or in the currency of the economy to which they export their goods (local currency pricing, LCP). In the former case, import prices change one to one with the exchange rate in the short-run. In the latter case, the short-run ERPT is zero. Hence, the resulting short-run pass-through in a sticky price model depends on the firms’ choice between LCP and PCP.

Bacchetta and van Wincoop (2005) try to endogenize the ERPT by modelling the currency pricing decision. They find two main factors determining this choice. The higher the market share of foreign firms in the domestic market, and the higher the differentiation between foreign and domestic products, the more likely foreign firms choose PCP. High market shares or highly differentiated products are associated with low competition. Thus, the competitive conditions influence the pass-through. Since the ERPT is high when many firms choose PCP, low international competition tends to increase the ERPT.2

In the paper of Corsetti and Pesenti (2004), the decision between LCP and PCP is linked to the exchange rate volatility. In their model, the degree of pass-through and the monetary policy are jointly determined. There are two equilibria: If firms choose PCP, the optimal policy of the monetary authorities is inward-orientated and consists in closing the national output-gap. This means that the countries choose different monetary policies, which leads to exchange rate volatility. But when exchange rates are volatile, the optimal decision of the firms is indeed to adopt PCP, which stabilizes their export mark-ups and implies a high ERPT. In the second equilibrium, the firms use LCP, implying a low ERPT. In that case, the optimal policies of the authorities of different countries coincide, leading to exchange rate stability. But if the exchange rate is stable, LCP is indeed one possible optimal pricing decision of the firms.

The relation between exchange rate volatility and ERPT is also addressed in Chang and Lapan (2003). Their paper is partial equilibrium in nature and studies a price com-petition game. Exchange rate variability affects the pricing strategies of the firms and thereby the ERPT. High exchange rate uncertainty creates incentives for the firms to

de-2_{Thus, the influence of competitive pressure on the ERPT is quite different from that in Dornbusch}

(1987) or Benigno and Faia (2010), where a more intensive competition increases the pass-through to import prices.

fer the price setting to be able to adjust prices to unexpected exchange rate fluctuations. This corresponds to PCP. Hence, similar to the result obtained by Corsetti and Pesenti (2004), Chang and Lapan (2003) find that the ERPT to prices is higher when exchange rates are volatile, because the firms more likely choose PCP in this case.

Another attempt to endogenize the ERPT consists in the analysis of the relation between monetary policy and the currency pricing decision. In a two-country general equilibrium model, Devereux and Engel (2001) find that monetary stability is a crucial factor determining the currency choice. With complete financial markets, prices are set in the currency of the country with the more stable monetary policy. With incomplete financial markets, there is an equilibrium in which all firms choose LCP. This is the case if the monetary policies of the two countries are similarly stable. But if there is a large difference in the volatility of monetary policy, goods are priced in the currency of the country with the more stable monetary policy. This analysis yields considerable implications for the ERPT: Countries with a stable monetary policy are likely to have their import prices set in their own currency, thus facing a low ERPT, whereas countries with an unstable monetary policy tend to have their import prices set in foreign currencies, which results in a high ERPT. This result is confirmed in the paper of Devereux et al. (2004). They stress the relevance of viewing the ERPT as endogenous. Changes in monetary policy can cause changes in the ERPT by affecting the firms’ currency pricing decisions. A country that stabilizes its money growth rate in order to stabilize domestic prices creates incentives for foreign exporters to set their prices in domestic currency. Therefore, such a country faces a low ERPT and its import prices become less sensitive to exchange rate shocks, which enhances overall price stability. As a consequence, Devereux et al. (2004) conclude that monetary authorities which take the ERPT as a given factor miss an important channel through which monetary policy works, namely the impact of monetary policy on the degree of the ERPT.

A further part of the literature deals with the fact that the ERPT is index specific. In particular, the ERPT to import prices may differ from the ERPT to consumer prices due to the presence of transportation and distribution costs on the one hand and of do-mestically produced goods and non-tradable goods on the other hand. Burstein et al. (2003a, 2005) demonstrate the underlying reasoning. The consumer price index (CPI) contains both prices of tradable and prices of non-tradable goods. Tradable goods can be divided into imported goods and domestically produced goods. Both domestic and imported goods rely on transportation and distribution services. The costs of these ser-vices describe the sum of expenditures which are necessary to sell a tradable good to a consumer, such as transportation costs, wages and rents in the wholesale and retail sec-tor and advertising costs. Burstein et al. (2003b) document that distribution costs are substantial. Thus, the ERPT to the CPI can be regarded as an aggregated response of prices to exchange rate shocks, which depends on the ERPT to the prices of imported

goods, domestically produced tradable goods, distribution and transportation services, and non-tradable goods. These considerations illustrate potential reasons for incomplete pass-through to consumer prices. For instance, if non-tradable goods represent a large part of the CPI and if the prices of these goods are relatively insensitive to exchange rate movements, then pass-through to the CPI will be low.

Allowing for distribution costs and non-tradable goods, Burstein et al. (2005) find that the substantial declines in real exchange rates after large devaluations are mainly due to slow adjustment of the prices for non-tradable goods and services. Corsetti and Dedola (2005) integrate distribution services in a two-country general equilibrium model. If non-tradable goods are required to distribute tradable goods to consumers, the price elasticity of demand becomes country-specific. As a consequence, monopolistic producers of tradable goods optimally charge different prices to domestic and foreign retailers. This dampens the response of both import and consumer prices to exchange rate movements, since the firms optimally adjust their mark-ups when faced with demand fluctuations. A different, but complementary approach is chosen by Bacchetta and van Wincoop (2003) who connect the firms’ currency pricing decision to the presence of non-tradable goods. In their model, imports are intermediate goods. Domestic firms use the intermediate goods to produce final goods. Competitive pressure on final goods producers is higher because they compete with all the goods bought by consumers (including non-tradable goods), whereas intermediate goods producers only compete among themselves. If the non-tradable sector is large enough, it is likely that intermediate goods producers choose PCP and final goods producers choose LCP. As a consequence, the ERPT to import prices is higher than the ERPT to consumer prices. Hence, this model highlights a complementary aspect since non-tradable goods do not matter because they are necessary to distribute imported goods to consumers, but because their presence affects the demand of consumers.

Finally, the study of Choudhri et al. (2005) explores the ability of a variety of new open economy macroeconomic models to explain the ERPT to different prices. Quantitative versions of the models are used to predict dynamic responses of prices to exchange rate shocks, which afterwards are compared with the empirical evidence. The models investi-gated in the study feature different combinations of aspects highlighted by the literature, such as sticky wages and prices, the currency pricing decision (LCP versus PCP) and distribution costs. The results indicate that the model which is most suitable to fit the data incorporates all these features: a combination of LCP and PCP (with roughly equal weights), sticky prices and wages, and distribution costs.

2.2

Empirical literature

The growing theoretical literature on the ERPT to prices has been accompanied by many empirical studies. This section presents an overview of some empirical papers using

dif-ferent methodologies for the estimation of the ERPT. A particular emphasis is put on results for Switzerland. Studies using single equation models for estimation are summa-rized in subsection 2.2.1. Subsection 2.2.2 presents papers estimating the ERPT with VAR models. The empirical literature that incorporates cointegration relations is ad-dressed in subsection 2.2.3. Finally, the empirical evidence for Switzerland is summarized in subsection 2.2.4.

2.2.1 Single equation models

Single equation models have been extensively used in order to estimate the ERPT to prices. They consist of a single equation with a price or inflation measure as depen-dent variable. The explanatory variables comprise the exchange rate (in level or first-differenced) and usually further control variables. To introduce dynamics into the model, lagged values of the exchange rate can be added as regressors.

Menon (1995) provides a survey of early contributions to the empirical literature on the ERPT. Most of these studies apply ordinary least squares (OLS) to estimate the ERPT. They have been criticized by Menon (1995) and more recent papers because they do not properly address the time series properties of the data. Many variables used to estimate the ERPT are non-stationary3 and the regression of an integrated variable4 on another integrated variable can be problematic. Such regressions can indicate a relation between the variables, although they are actually independent. This phenomenon is known as spurious correlation.

As a consequence of this criticism, more recent studies attempt to adequately incorpo-rate the time series properties of the data. Gagnon and Ihrig (2004) estimate the ERPT to consumer price inflation in 20 industrial countries. Since they use first-differenced data for prices and exchange rates, non-stationarity can be rejected for a majority of countries. Hence, the estimates of the ERPT should not be subject to spurious correlation for most of the countries. The results of Gagnon and Ihrig (2004) suggest that the pass-through to consumer prices is low. On average, a one percent depreciation of the local currency leads to an increase of consumer prices by 0.23% in the long-run. There is substantial variation across countries. The estimate for Switzerland is smaller than the average (the point estimate suggests a CPI change by 0.15% in the long-run) and not significantly different from zero. The overall results of the study show that the ERPT to consumer prices has declined over time.

3_{A time series process X}

t is stationary if the expectation of Xt is constant, the variance of Xt is finite

and the covariance betweenXtandXs,Cov(Xt, Xs), is equal to the covariance betweenXt+randXs+r, Cov(Xt+r, Xs+r), i.e. the covariance depends on the time lag betweent and s, but is independent of

the specific points in timetand s(Neusser (2006), p. 12).

4_{A time series process X}

t is integrated of order d if the d-times differenced time series is stationary.

For a formal definition see Neusser (2006), pp. 99-100. According to this definition, a trend-stationary process, i.e. a process that is non-stationary because its expectation is a function of the time and that becomes stationary if the time trend is subtracted, is not an integrated process.

Campa and Goldberg (2005) estimate the ERPT to import prices for 23 OECD coun-tries and analyze its determinants. Because tests indicate that most of the time series may have a unit root but are not cointegrated, they choose to apply OLS with variables in log differences. Price changes are regressed on current and lagged exchange rate changes, the domestic GDP growth rate and the current and lagged changes in the costs of foreign exporters. The ERPT to import prices is defined as the elasticity of import prices with respect to the exchange rate, keeping the change of foreign exporters’ costs and domes-tic GDP growth constant. On average, the estimated ERPT amounts to 0.46 over one quarter and to 0.64 over five quarters. The estimates for Switzerland are larger: The elas-ticities amounts to 0.68 and to 0.93, respectively. The latter is not significantly different from one. Thus, full pass-through to Swiss import prices over the long term cannot be rejected. Using disaggregated data, Campa and Goldberg (2005) show that the ERPT differs across goods, but is stable over time for the separate product categories. Therefore, they conclude that changes in the composition of imports are an important explanation for changes in the ERPT to overall import prices over time.

Single equation models have the advantage of being relatively easy to estimate and to interpret. However, there are some substantial drawbacks of these models. Firstly, they consider only one price index at a time. Since only a single equation is estimated, it is impossible to jointly analyze the behaviour of import and consumer prices in the aftermath of an exchange rate shock. Secondly, they rely on the strong assumption that exchange rate changes and the other explanatory variables (for example GDP) are exogenous. These models feature an endogeneity problem because price changes may affect GDP and future exchange rate changes. Therefore, it is more adequate to use models allowing for extensive dynamic interactions between the variables of interest, such as VAR models.

2.2.2 Vector autoregressive models

In recent years, structural VAR models have been extensively used in order to estimate the ERPT to prices. In contrast to single equation models, VAR models can contain several price indices and allow for complex interrelations between the variables. Moreover, they are more suitable to capture the dynamics of the ERPT. A large majority of the studies using VAR models applies a recursive scheme (Cholesky decomposition) for the structural identification of the model.

McCarthy (2000) examines the impact of exchange rate and import price fluctuations on producer and consumer prices in nine industrialized economies. He uses a structural VAR model with a distribution chain of pricing, incorporating three stages of inflation (import, producer and consumer price inflation). This framework allows tracking the ERPT to each stage of prices, which may give additional insight into the complex transi-tion mechanism from exchange rates to final consumer prices. Oil price inflatransi-tion, output gap, money growth and the short-term interest rates are included as additional variables.

The results show that while an appreciation of the exchange rate has a negative short-run impact on import prices, there is no significant effect on producer and consumer prices in most of the economies (including Switzerland).

Using a slightly different model, Hahn (2003) finds a significantly negative response of euro area prices to an appreciation shock. The size of the response and the speed of adjustment decrease along the distribution chain of pricing; they are largest for import and lowest for consumer prices. An appreciation shock of one percent reduces import, producer and consumer prices by about 0.5%, 0.3% and 0.16%, respectively.5

There are further studies documenting that the ERPT decreases along the distribution chain. Faruqee (2004) presents additional evidence on the ERPT to euro area prices. The hypothesis of full pass-through to import prices in the long-run cannot be rejected. The response of producer and consumer prices is much lower: An appreciation shock of one percent decreases these price indices by roughly 0.2% and 0.1%, respectively. Core inflation and wages show hardly any reaction to an exchange rate shock. The response of export prices is considerable, but less pronounced than the reaction of import prices. Consequently, the terms of trade increase with a currency appreciation. Similar findings are reported in Choudhri et al. (2005) for six major industrial countries. The responses of import and export prices are stronger than those of producer and consumer prices. Wages show no significant response. Since the reaction of import prices exceeds the one of export prices in the short- and medium-term, the terms of trade temporarily increase in the aftermath of an appreciation shock. Ito and Sato (2006) analyze the ERPT for East Asian countries. They find a huge ERPT to import prices. The response of producer prices is lower, but still sizable, whereas the reaction of consumer prices is moderate and for some countries not significantly different from zero.

A few studies analyze the transmission mechanism from exchange rates to prices in more detail by estimating the ERPT to prices of specific categories of goods. Belaisch (2003) uses VAR models to estimate the ERPT to various price indices in Brazil. The study explicitly distinguishes between tradable and non-tradable goods. The findings reveal that prices of the former react more quickly. However, in the long-run, the price change is similar for both types of goods. Overall, the estimates indicate incomplete pass-through to all price indices except wholesale prices. The ERPT declines along the distribution chain. In a study using Swiss data, Stulz (2007) finds evidence for significant but incomplete ERPT to import and consumer prices. The impulse response functions reveal a quick and somewhat hump-shaped reaction of import prices to an exchange rate shock whereas consumer prices slowly converge to their new long-run level. The long-run ERPT elasticities amount to 0.37 and 0.18 for import and consumer prices, respectively. Furthermore, consumer prices are divided into prices of imported goods and the remaining

5_{These price changes are the accumulated impulse responses measured three years after the shock}

goods. The ERPT to consumer prices of imported goods is estimated. The results indicate a long-run ERPT elasticity of 0.34. Interestingly, this is very close to the pass-through to import prices, suggesting that rigid import prices rather than distribution costs are the main reason for incomplete ERPT to consumer prices of imported goods. However, this result does not hold in a more recent subsample which is characterized by an environment of low and stable inflation. In this subsample, the ERPT is lower for all price indices and, especially, consumer prices of imported goods barely react to exchange rate shocks. As a consequence, the ERPT to overall consumer prices is virtually zero.

Finally, Cavaliere (2007) analyzes the ERPT to different price indices in 20 indus-trialized economies, including Switzerland. The results show a significant reaction of import prices to exchange rate shocks for all countries. There is an immediate jump in import prices followed by a quick adjustment to the new long-run level. For most of the economies, including Switzerland, the long-run elasticity of import prices with respect to the exchange rate is close to one, indicating almost full pass-through. The responses of consumer prices are considerably lower and, for some countries, not significantly different from zero. The long-run ERPT elasticity is smaller than 0.5 for many countries, but it is larger for Switzerland. The adjustment process of consumer prices is slower and more prolonged compared to that of import prices. The results of the study reveal that high ERPT to import prices does not necessarily imply high pass-through to consumer prices. The responses of producer prices are an intermediate case; for some countries, the reaction is more similar to that of import prices, for other countries (including Switzerland), the response function resembles the one of the CPI.

Overall, the empirical evidence on the ERPT from VAR models can be summarized as follows. Firstly, the magnitude of the ERPT and the speed of adjustment decrease along the production and distribution chain. Secondly, the pass-through to producer and consumer prices seems to be incomplete and sometimes not significantly different from zero. Third, the ERPT to import prices is significant, but the results are mixed whether there is full or limited pass-through.

Structural VAR models are suitable for the consistent estimation and the analysis of dynamic adjustments of interrelated variables to various shocks. However, there is a substantial drawback of these models. Since many variables involved in the analysis of the ERPT are non-stationary, they have to be first- or even second-differenced in order to achieve stationarity. This way of proceeding results in the loss of the information contained in the level of the variables. This can be problematic if there are long-run equilibrium relations between the variable levels, which are neglected when the analysis is restricted to changes in the variables.

2.2.3 Cointegration analysis and vector error correction models

Cointegration analysis has the advantage of incorporating short-run dynamics without disregarding long-run equilibrium relations among variables. Hence, it comprises the advantages of VAR models and in addition incorporates the information contained in the level of the time series. In the light of these features, it is somewhat surprising that there are only few studies estimating the ERPT in a cointegration framework. While some studies are not able to find evidence for cointegrating relations and, as a consequence, use single equation or VAR models, there are several empirical studies that disregard cointegrating relations without even testing for them. The concept of cointegration is described in subsection 4.1.1. A frequently used model in this context, the VEC model, is introduced in subsection 4.1.2.

The empirical analysis by Kim (1998) uses cointegration analysis with a VEC model to estimate the ERPT to US producer prices. He finds one cointegrating relation between US producer prices, exchange rates, money supply, income and interest rates. The exchange rate has a significant, but rather small long-run impact on prices; keeping the other variables constant, an appreciation of the US dollar by one percent decreases producer prices by only 0.24%.

Billmeier and Bonato (2004) use both a VAR model and a cointegration approach to assess the ERPT to prices in Croatia. The test for cointegration indicates one cointe-grating relation between the exchange rate, the manufacturing and the retail price index. The cointegrating relation reveals a significant but incomplete ERPT to retail prices: A devaluation of one percent increases retail prices by about 0.3% in the long-run.

A more detailed study is presented by Masten (2004), who explicitly addresses the issue of identification of the equilibrium pass-through effect in a cointegration framework. His work is based on the paper of Johansen (2002) about the interpretation of cointegrating coefficients. Johansen (2002) shows that, under certain conditions, a method similar to the instrumental variables approach can be applied to cointegrating relations. Instead of using a change in the exogenous instrumental variables to produce the desired changes in the endogenous variables, there may be changes in the current values of the time series that will induce long-run changes of the desired form. For example, in the context of the ERPT to prices, the desired modifications would be a long-run change in the exchange rate by one percent and the resulting percentage price change, keeping the other variables in the cointegrating relation constant. Johansen (2002) proves the conditions under which such a counterfactual experiment is possible and, hence, under which the cointegrating coefficients can be interpreted as long-run elasticities (provided that the variables are measured in logarithms). Masten (2004) uses these findings in order to estimate the ERPT for Hungary, Poland, Slovenia and the Czech Republic. The long-run equilibrium pass-through derived from the cointegrating coefficients is remarkably high. For Slovenia

and Hungary, the ERPT to consumer price inflation is virtually one, meaning that CPI inflation changes one to one with the growth of the nominal exchange rate. The estimate for Poland is somewhat smaller, but not significantly different from one either. The results for the Czech Republic suggest a long-run ERPT of about 0.6.

2.2.4 Summary of the empirical evidence for Switzerland

Table 1 summarizes the results of some empirical studies estimating the ERPT for Switzer-land. The empirical evidence suggests that the degree of pass-through decreases along the distribution chain. Regarding import prices, the estimates vary between a long-run pass-through elasticity of roughly 0.2 and 1. The response of import prices seems to hap-pen rather quickly and to be mostly accomplished one year after the shock occurred. The ERPT to producer and consumer prices is either incomplete or not significantly different from zero. With regard to consumer prices, the estimates range from a pass-through of virtually zero to a long-run ERPT elasticity of more than 0.5. The CPI adjusts more slowly than import prices to exchange rate shocks. The instantaneous reaction is very small. Afterwards, the accumulated impulse response function converges to the new long-run level. Some studies present evidence for a decrease in the ERPT over time. This decline is rather small with regard to import prices, but it is substantial regarding the ERPT to the CPI.

study method findings

Gagnon and Ihrig (2004) single equation The results indicate that a depreciation of 1% leads to an increase in consumer prices by 0.15% in the long-run. However, this increase is not significantly different from zero.

Campa and Goldberg (2005) single equation Import prices change by 0.68% over one quarter and by 0.93% over five quarters given a 1% change in exchange rates. Both estimates are significantly different from zero. The latter is not significantly different from one. McCarthy (2000) VAR The ERPT to import prices is significant in the first year

after the exchange rate shock. The pass-through to pro-ducer and consumer prices is not significantly different from zero.

Stulz (2007) VAR An exchange rate shock of 1% leads to a change in im-port prices of 0.35% after one quarter and of 0.37% two years after the shock occurred. Consumer prices change by 0.09% and 0.18%, respectively. The ERPT to con-sumer prices for imported goods amounts to 0.27% and 0.34% after one quarter and two years, respectively. Cavaliere (2007) VAR The long-run ERPT elasticity with respect to exchange

rate shocks is close to one for import prices, amounts to about 0.5 for producer prices and lies between 0.5 and one for consumer prices.

3

Theoretical analysis

3.1

A theoretical model of international strategic pricing

Section 2.1 has shown the importance of imperfect competition for the ERPT. The findings of Krugman (1986) and Dornbusch (1987) have been the basis for further theoretical and empirical studies. This section discusses a more modern model. It is a simplified version of the model presented in Benigno and Faia (2010). The simplification consists in omitting the distinction between different sectors. The original assumption that firms are not small with respect to their sector and that their pricing decision affects the sectoral price index is replaced by the assumption that firms are not small with respect to the economy and that their pricing decision influences the overall price index of the economy. Appendix A shows the details of the derivation of some equations used in this section.

The setup of the model is as follows. There are two countries, labelled domestic economy and foreign economy. In the domestic economy, there areN different goods. Nh

goods are produced by domestic firms and the remaining Nf _{by foreign firms. There is a}

representative household maximizing the present discounted value of utility. Utility is a function of a composite consumption goodCtwhich is an aggregate of all available goods.

The aggregation of the goods occurs according to the Dixit-Stiglitz aggregator:

Ct=   N X j=1 C θ−1 θ j,t   θ θ−1 . (2)

Cj,t denotes the consumption of good j in period t. θ is the elasticity of substitution

across goods. In this model, each firm is a monopolistic supplier of its good. However, households are able to substitute between the goods, which limits the monopoly power of the firms.

Since utility in period t depends on the composite consumption good Ct, households

choose Cj,t such as to minimize expenditure for the desired amount of Ct. The solution

to this minimization problem yields the following demand function for a generic good j:

Yj,t = _P j,t Pt −θ Yt. (3)

Yt is the overall demand of the domestic economy, Pj,t is the price of good j and Pt is

the overall price index, defined as the minimum expenditure needed to buy one unit of

Ct and given by the following equation:

Pt=   N X j=1 P_j,t1−θ   1 1−θ . (4)

The aim of the firms is to maximize profits. For simplicity, the production function is assumed to depend only on labour Lt and to be of linear form:

domestic firm i: Yi,t =AhtLi,t, (5)

foreign firm j: Yj,t =AftLj,t, (6)

in which Ah

t and A

f

t are productivity parameters.

Under flexible prices, each firm chooses its price to maximize profits. The profit function of a domestic firm i in period t is characterized by the following equation:

Πi,t =Pi,tYi,t−WthLi,t. (7)

W_th is the nominal wage in the domestic economy in period t. Using the production function (5) to replace Li,t and replacing Yi,t by the demand function (3), profits can be

rewritten as follows:

Πi,t =Pi,tYi,t −Wth

Yi,t Ah t = Pi,t− Wh t Ah t ! Pi,t Pt −θ Yt. (8)

Assuming that foreign firms set their prices in the currency of the country in which the products are sold, profits in foreign currency of a foreign firm j in period t are given by the following equation:

Π∗_j,t = Pj,t St Yj,t−Wf ∗ t Yj,t Aft = Pj,t St −W f∗ t Aft ! Pj,t Pt −θ Yt. (9)

Variables denoted with a∗ are denominated in foreign currency. W_tf∗ is the nominal wage in the foreign labour market in period t. St denotes the nominal exchange rate.

Both domestic and foreign firms maximize their profits with respect to their price, taking into account that they are not small with respect to the market and, as a conse-quence, that their pricing decision affects the overall price index.6 _{The optimal prices set}

by domestic and foreign firms are characterized by the following equations:

domestic firm i: Pi,t =

θ(1−ψi,t) θ(1−ψi,t)−1 Wh t Ah t (10) foreign firm j: Pj,t = θ(1−ψj,t) θ(1−ψj,t)−1 Wtf∗ Af_t St (11) ψi,t ≡ ∂Pt ∂Pi,t Pi,t Pt (12)

For the interpretation of these equations, it is important to recognize that the elasticity

6_{The paper of Benigno and Faia (2010) uses an alternative assumption, namely that the firms are able}

of the price index with respect to the price of a generic firm i,ψi,t, is exactly equal to the

market share of firm i (see Appendix A).

Consider the special case that the market share of each firm goes to zero. In this limiting case, firms are small with respect to the market and their pricing decision does not affect the overall price index of the economy. Setting ψi,t = 0, equation (10) becomes

the familiar mark-up pricing formula7_:

Pi,t = θ θ−1 Wh t Ah t . (13)

Prices set by domestic firms are a mark-up over marginal costs. The mark-up depends on θ, the elasticity of substitution across the goods. A very similar formula is obtained for the prices of foreign firms:

Pj,t = θ θ−1 W_tf∗ Aft St. (14)

The price setting formulas (13) and (14) show that the prices of domestic firms are independent of the exchange rate whereas the elasticity of the prices of foreign goods with respect to the exchange rate is equal to one. Hence, this special case of the model yields the strong prediction that import prices should change one to one with the nominal exchange rate whereas the ERPT to prices of domestically produced goods is zero.

In the general case, in which the firms are aware that their pricing decision influences the overall price index (equations (10) and (11)), the optimal prices of domestic and foreign goods are still a mark-up over marginal costs. However, the mark-up is not constant any more. It depends positively on the market share ψi,t. Because of that, the mark-up

depends negatively on the price set by a firm: If a firm unilaterally increases its price, it will loose market share and the mark-up decreases.

The dependence of the optimal prices on the market share introduces strategic inter-action between domestic and foreign firms. Suppose that there is an appreciation of the domestic currency (St decreases). The direct effect consists in foreign firms lowering their

prices, since their marginal costs in domestic currency decline. Ceteris paribus, the lower price increases the market share of foreign firms to the detriment of domestic firms. The decline in market share of domestic firms causes a reduction of their mark-up, meaning that domestic firms lower their prices as well in order to limit their loss of market share. The strategic interaction between domestic and foreign firms is crucial for this result. Eventually, both domestic and foreign firms lower their prices in response to an apprecia-tion: foreign firms due to lower marginal costs and domestic firms because they compete with the foreign firms in the domestic market.

To calculate the ERPT that is implied by this general case of the model, a log-linear

7_{The same formula results if the model is designed as a monopolistic competition model with a continuum}

approximation of the equations (10) and (11) combined with the definition of the market share is taken (see Benigno and Faia (2010), pp.7). This leads to the following equations:8

c Pt h = κs f 1 +κ d Wt f∗ −Ac_t f +Sc_t + 1 +κs h 1 +κ d Wt h −Ac_t h (15) c Pt f = κs h 1 +κ d Wt h −Ac_t h + 1 +κs f 1 +κ d Wt f∗ −Ac_t f +Sc_t (16) with κ= θ−1 θ1− 1 N −1 1 N −1, s h ₌ Nh N and s f ₌ Nf N

Variables with a hat denote log-deviations from the steady state. sh _{and s}f _{denote the}

respective share of domestic and foreign firms relative to the total number of firms. From these equations, it is obvious that the prices of both domestic and foreign firms depend on the exchange rate.

The impact of exchange rate movements on the price of imported goods is given by the term 1+κsf

1+κ . Thus, pass-through to import prices is usually less than one. The two

exceptions are the absence of domestic firms (sf _{= 1, in which case foreign firms can}

pass through exchange rate movements without losing market share) and the case of monopolistic competition (N goes to infinite and therefore κ goes to zero). Hence, this model predicts a higher ERPT to import prices for countries with a larger share of imports and with a higher degree of competition (a higher N). These results coincide with those from the Cournot model in Dornbusch (1987).

The analysis of the prices of domestically produced goods (equation (15)) reveals that an increase of cS_t raises Pc_t

h

by ₁₊κsf_κ. Hence, competition from abroad influences domestic prices: They react to exchange rate movements, but the reaction is certainly lower than one. The extent of the price change depends positively on the share of imported goods and negatively on the degree of competition (characterized by N).

The implications of this theoretical model can be summarized as follows. Firstly, import prices react to exchange rate movements, but incompletely. Secondly, even the prices of purely domestic goods, i.e. goods not relying on any imported inputs, react to exchange rate shocks because domestic firms compete with foreign firms. This is modelled as actual competition, but potential competition through the threat of market entry might also play a role. Finally, the model confirms the findings of the literature that the share of imports and the degree of competition are important determinants of the ERPT. A higher import share increases the sensitivity of both import and domestic prices with respect to exchange rate changes. A more intensive competition increases the pass-through to import prices, but it reduces the response of domestic prices to the exchange rate.

8_{Since all domestic firms are equal and face the same problem, they will set the same price. The same}

is true for the foreign firms. Therefore, the indices indicating the firms are dropped. To distinguish between the price of domestic and foreign goods, the superscriptshandf are used.

3.2

Implications of the theoretical analysis

The preceding sections 2.1 and 3.1 have analyzed the ERPT to prices theoretically. This section briefly summarizes some of the theoretical implications that arise from the above analysis and that are of importance for this master thesis.

The theoretical models yield several concrete and testable predictions regarding the ERPT. The following issues are addressed for the Swiss economy in the empirical part of this paper (section 6):

• The ERPT to consumer prices is positive, but incomplete. This is suggested by the model of international strategic pricing (section 3.1). Thus, the elasticity of the CPI with respect to the exchange rate should be located strictly above zero and below one.

• The ERPT to import prices is positive. Whether the pass-through is limited or complete depends on the model.

• Although some models claim that the prices of domestically produced goods are independent of the exchange rate, there are two reasons to believe that these prices react to exchange rate movements, albeit to a lower extent than import prices. Firstly, domestically produced goods usually rely partially on some imported in-puts. As a consequence, their price depends to some extent on import prices, and since import prices depend on exchange rates, so do the prices of domestic goods. Secondly, the model of section 3.1 shows that even the prices of purely domestically produced goods depend on the exchange rate, because domestic firms compete with foreign firms whose marginal costs (and hence whose prices) hinge on the exchange rate.

• Price stickiness requires a dynamic analysis of the ERPT. With sticky prices, the ERPT to domestic prices is low in the short-run and increases only in the course of time when prices can be adjusted. Moreover, the short-run ERPT to import prices is mostly determined through the currency pricing decision. If LCP dominates, the short-run pass-through tends to zero. In contrast, the ERPT is close to one if PCP dominates. Thus, pass-through in the short-run may be largely determined through price rigidities. A dynamic analysis is necessary in order to assess how the ERPT evolves over time as prices can be adjusted.

• The ERPT is likely to be different for distinct price indices due to the presence of non-tradable goods as well as transportation and distribution costs. Usually, the ERPT is assumed to be largest for import prices at the border level and to decrease along the production and distribution chain down to the lowest pass-through for retail prices, since those prices contain the largest portion of distribution costs.

Moreover, due to the presence of non-tradable and of domestic tradable goods, whose prices are likely to react less than import prices to exchange rate movements, the ERPT to the CPI is lower than the ERPT to import prices.

4

Methodology, model and identification

4.1

Methodology

This section explains the methodology which is used in the empirical part of this paper. Subsection 4.1.1 describes the concept of cointegration. VAR and VEC models are intro-duced in subsection 4.1.2. Subsections 4.1.3 and 4.1.4 present the tests for cointegration and unit roots. Particular emphasis is put on the calculation of the impulse response func-tions (subsection 4.1.5), since the ERPT is essentially given by these funcfunc-tions. Finally, the issues of inference and bias are addressed in subsection 4.1.6.

4.1.1 Cointegration

Many economic time series are non-stationary. As discussed in section 2.2, the problem of spurious correlation may occur in regressions of an integrated variable on another integrated variable. Therefore, time series are usually transformed in order to achieve stationarity, for example by differencing the series. However, this results in the loss of information contained in the level of the variables. This problem can be solved if the time series are cointegrated. This is the case if there is a linear combination of the time series that is stationary, although the series are non-stationary.

Cointegration is defined as follows (Neusser (2006), p. 218):

Definition: Cointegration The multivariate time series process{Xt}is cointegrated if

{Xt} is integrated of order one and if there is a vector β ∈Rn, β 6= 0, such that {β0Xt}

is stationary, given an appropriate distribution of the starting value X0.

β is called cointegrating vector. The cointegration rank r is the maximal number of linearly independent cointegrating vectors β1, . . . , βr. These vectors span a vector space,

the so-called cointegration space.

These stationary linear combinations of the integrated series, calledcointegrating equa-tions or cointegrating relations, can be interpreted as long-run equilibrium relations be-tween the variable levels. Because the cointegrating equations are stationary, deviations are of temporary nature. Shocks cause deviations from these equilibrium relations, but these deviations cause adjustments of the variables in order to restore the equilibrium relations in the long-run.

If there are cointegrating relations, it is reasonable to include them in the model used for estimation. This does not cause spurious correlation since these relations are

station-ary combinations of the time series. Since VEC models incorporate the cointegrating relations and therefore provide a possibility to allow for level effects, this master thesis uses these models for the estimation of the ERPT. In contrast, differencing the series to achieve stationarity would result in the loss of the information contained in these long-run equilibrium relations between the variable levels.

4.1.2 VAR and VEC models

A large part of the empirical literature uses VAR models to estimate the pass-through to prices (see subsection 2.2.2). These models are of the form

Xt=c+ Φ1Xt−1+. . .+ ΦpXt−p +Zt, Zt∼WN(0,Σ), (17)

with constant column vector c and coefficient matrices Φ1, . . . ,Φp, where p denotes the

order of the model. Zt is a white noise process with mean zero and covariance matrix Σ.

To avoid the problem of spurious correlations, these models are usually estimated with time series that have been stationarized. As discussed above, this results in the loss of the cointegrating relations.

In contrast, the VEC model preserves the cointegrating equations between the time series. The VEC model can easily be derived from a VAR model which is estimated using variables that are integrated of order one. Subtracting Xt−1 from the VAR(p) model in

equation (17) yields a VEC model of order p−1:

∆Xt=c+ ΠXt−1+ Γ1∆Xt−1+. . .+ Γp−1∆Xt−p+1+Zt. (18)

The coefficient matrices of the VEC model in equation (18) are related to the coefficient matrices of the VAR model in equation (17) as follows: Γi =−Ppj=i+1Φj. Π is given by

Π =−In+ Φ1+. . .+ Φp, where In denotes the identity matrix andn denotes the number

of variables in the model.

The term ΠXt−1in equation (18) is crucial since this term makes the difference between

a VAR model estimated with differenced data and a VEC model. Suppose that Π is singular with rank r, 1 ≤ r < n. In this case, there are at least n −r unit roots and there are two n×r matricesα andβ with full column rankr such that Π =αβ0 (Neusser (2006), p. 219).9_{. Using this equality, the VEC model can be rewritten as follows:}

∆Xt=c+αβ0Xt−1+ Γ1∆Xt−1+. . .+ Γp−1∆Xt−p+1+Zt. (19)

The columns of β are the cointegrating vectors. Thus, the cointegrating equationsβ0Xt−1

enter the VEC model. Matrix α is called loading matrix.

9_{The decomposition of Π in the product ofαandβ}0 _{is not unique. For any non-singularr×rmatrixR,}

The representation in equation (19) is useful to understand the mechanisms which gave rise to the term vector error correction model10. Since β0Xt is stationary, Eβ0Xt can

be interpreted as steady state of the system or long-run equilibrium relation. Deviations from this equilibrium (errors) lead to adjustments (corrections) in ∆Xt. The loading

matrix α determines how ∆Xtadjusts to deviations in the cointegrating relations. These

adjustments result in restoring the equilibrium in the long-run.

4.1.3 Tests for cointegration

Since the main difference of a VEC model to a VAR model estimated with differenced data consists in the inclusion of the cointegrating relations, these relations should be tested for. If there are none, it is sufficient to use a VAR model. Otherwise, a VEC model might be more appropriate for estimating the ERPT.

This paper uses the Johansen test, a likelihood ratio test, to test for cointegration. There are two types of the test. These types are distinguished by the alternative hypoth-esis that is applied. Let H(j) denote the hypothesis that there are at most j linearly independent cointegrating vectors.

In the trace test, the alternative hypothesis is always H(n), where n is the maximal number of cointegrating relations, which is given by the number of time series in the model. A sequence of hypotheses is tested. Firstly, the null hypotheses of zero cointe-grating relations (H(0)) is tested versus the alternative H(n). A failure of rejectingH(0) indicates that there are no cointegrating relations. If H(0) is rejected, there is at least one cointegrating relation. Then, the next step of the sequence tests H(1) against H(n). If the test cannot reject H(1), there is one cointegrating relation. Otherwise, there are at least two cointegrating relations and H(2) is tested against H(n) as a next step. This procedure is carried on until the test fails to reject a null hypothesis.

Themax test applies a similar sequential testing strategy. In each step of the sequence,

H(j) is tested against H(j + 1). The sequence starts with testing H(0) against the alternative H(1). A failure of rejecting H(0) indicates that there is no cointegrating relation. In contrast, if the test rejects H(0), there is at least one cointegrating equation and H(1) is tested against H(2) as a next step. This procedure is carried on until the test fails to reject a null hypothesis.

Before the Johansen test can be applied, a model has to be specified because the asymptotic distribution of the test statistics depends on the specification of the deter-ministic part of the model (Neusser (2006), pp. 227-228). Since the data used in this master thesis exhibit a trend, there are two options. Both of them contain a constant in the cointegrating equation. The difference between the options consists in whether a time trend is included in the cointegrating equation.

For the models estimated in this paper, a time trend is included in the cointegrating equation for several reasons. First of all, both theoretical considerations and empirical studies show that the ERPT to prices can change over time. Hence, one should allow for time variation also within the cointegrating equation. Secondly, if some of the series are trend-stationary, the cointegrating equation should include a trend. As section 6.1 shows, evidence is unclear whether the exchange rate index has a unit root or is trend-stationary. As a consequence of this potential trend-stationarity, it might be safer to include a time trend in the cointegrating equation. Finally, allowing for a time trend amounts to the estimation of a more flexible model from an econometric point of view. Since there is no empirical or theoretical reason to a priori impose the restriction that there is no time trend, the more flexible model is chosen.

In addition to the deterministic specification of the model, the number of lags of the first-differences of the endogenous variables needs to be determined before the cointe-gration tests. In this master thesis, the following approach is used. A VAR model is estimated first. Different specifications of the VAR model are analyzed with respect to information criteria11_{, the significance of the coefficients and the residuals. The number}

of lags chosen for this VAR model is then transformed into the VEC framework12 _used

for the cointegration test.

4.1.4 Tests for unit roots

Consider the VEC model as in equation (19). To avoid the problems of regressing an integrated variable on another, ∆Xt should be stationary. This means thatXtshould not

be integrated of order two or higher. Therefore, the first step of the empirical analysis consists in testing for unit roots. If the tests indicate a higher order of integration, then the time series are transformed before the estimation of the model such that Xt is integrated

of order one and ∆Xt is stationary.

This master thesis uses two unit root tests: the augmented Dickey Fuller (ADF) test and the Phillips Perron (PP) test. Both tests are based on the regression of Xt onXt−1

and some deterministic components. The ADF test includes lags of ∆Xt−1 as additional

regressors. In contrast, the PP test addresses the autocorrelation in the data by correcting the estimator or its t value after the estimation in a non-parametric way.

The PP test has several advantages compared to the ADF test. It is more general than the ADF test due to its non-parametric correction for autocorrelation. Moreover, an exact modelling is not necessary. In addition, the PP test is more powerful, i.e. it has a higher probability of rejecting the unit root hypothesis if it is wrong in fact. However,

11_{The following information criteria are considered: the Akaike Information Criterion (AIC), the Bayesian}

Information Criterion (BIC) and the Hannan Quinn Information Criterion (HQ)

12_{As shown in the previous subsection, a VAR model of orderpcan be rewritten as VEC model of order}

the PP test has a more pronounced size distortion, which results in too many rejections of the null hypothesis (Neusser (2006), p. 113).

4.1.5 Impulse response functions

In this master thesis, the ERPT to a particular price index is defined as the percentage change of this price index in response to a one percent exchange rate shock. Thus, the ERPT is basically an impulse response function and is computed accordingly.

As shown in subsection 4.1.2, a VAR model of order p in levels can be written as a VEC model of orderp−1 and vice versa. Hence, the computation of the impulse response functions of a VEC model is analogous to that of a VAR model, for which the impulse response functions are given by the infinite moving average representation of the model (Neusser (2006), pp. 193-194):

Xt=Zt+ Ψ1Zt−1+ Ψ2Zt−2+. . . ,

= (In−A)−1BVt+ Ψ1(In−A)−1BVt−1+ Ψ2(In−A)−1BVt−2+. . . . (20)

The matrices Ψ1,Ψ2, . . . are computed using the estimated coefficients of the VEC model

by the method of equating coefficients. The second equation uses the relation between the structural form of the model,

Xt=AXt+ Ω1Xt−1+. . .+ ΩpXt−p+BVt, (21)

and the reduced form, which is given by the VAR representation of the model:

Xt = Φ1Xt−1+. . .+ ΦpXt−p+Zt. (22)

Subsection 4.3 will discuss the identification strategy used to obtain the coefficients of the structural form given the estimated coefficients of the reduced form. Once the matrices

A and B are known, the impulse response functions are given by the coefficients of the matrices [Ψj(In−A)−1B], j = 0,1,2, . . ..

The impulse response functions show the changes of the time series in response to an exchange rate shock. For the time series in logarithms, the impulse response functions directly measure the percentage change of the time series after an exchange rate shock. Thus, the ERPT is given by the impulse response functions that are normalized such that they represent the response to an exchange rate shock of one percent.

4.1.6 Inference and bias-correction

The previous subsection explained how to compute the ERPT given an estimated VEC model and a suitable identification strategy. To assess the precision of the estimates and

to cond